This invention is an improvement on the equalizer networks and methods of developing scaling coefficients therefor of Peters U.S. Pat. No. 4,566,119, which defines an equalizer and discusses implementations thereto, specifically, Davis, Weiner and Lee, and Tattersall, describing the shortcomings of each. The equalizer networks described in U.S. Pat. No. 4,566,119 are based on a set of minimum phase transversal filters derived from a single active element all pass chain, each of the filters consisting of the summation of scaling circuit outputs from the all pass chain, the outputs of the filters being scaled and summed to provide the adjustable equalizer realization. An equalizer as described thus offers virtually ripple-free frequency response with minimal interaction from band to band and a reasonable approximation of the desired frequency response. It was stated in U.S. Pat. No. 4,566,119 that calculations involving both the real and imaginary components of the Fourier series were unwieldy and indeed "virtually impossible" due to a non-linear relationship between the frequency response and the scaling coefficients. Thus a linear approximation to the requested frequency response, calculated only from the real component of the series, was implemented.
While the method disclosed in U.S. Pat. No. 4,566,119 is of great utility, it is subject to some shortcomings. The method of determining the scaling coefficients produces a linear approximation to the real part of the desired frequency response and forces the imaginary part to follow by imposing minimum phase constraints. Hence, the selectivity (Q) of the equalizer filters is compromised. In addition, the method used forces equal errors in the pass band and stop band when measured arithmetically, resulting in response curves which are not reciprocal (mirror image) in stop band (cut) and pass band (boost) response when measured in decibels.